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Further Kinematics

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  Edexcel IAL Mechanics 3 (WME03)

Further Kinematics

The big idea: When acceleration depends on displacement, write it as v dv/dx; when it depends on time, as dv/dt; then separate and integrate.

Summary — What This Chapter Covers
  • a = dv/dt = v dv/dx = d2x/dt2.
  • Use v dv/dx when a is a function of x.
  • Use dv/dt when a is a function of t or v.
1. Acceleration as a Function of Time, Displacement or Velocity
Variable a

Choosing the right form of a

Pick the form of a that contains the variable a depends on, separate variables, integrate, and use the given conditions.

Worked Example

A particle has a = 3x2 m s−2 (x ≥ 0) and v = 2 m s−1 at x = 0. Find v when x = 2.

Practice Question

a = −kv. Show that v = Ue−kt, where U is the initial speed.

Memorise
a(x)

v dv/dx

a(t)

dv/dt

a(v)
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